Refutation to 1. d4 2. Nf3 3. g3 system...

It's not a refutation. Apart from the fact that your opponent played a very weird opening (mixing up the London and Catalan), something else instead of the horrendous 14.Kh1?? like 14.Nf3 would have left him only slightly worse.

@SavageAntarctican When you have the bishop on g2 you want to play c2-c4 in one move. The point is to try to target the light squares in the centre. It's just like in the Dragon Sicilian, but on light squares instead of dark squares. So responding to 5...c5 with 6.c3? was already a serious mistake. Instead, you should play 6.c4!, maximizing the power of your light-squared bishop, and opening up the centre at a moment when you have a lead in development (you are castled and your opponent is far from being castled).

After that, you went on to put the dark-squared bishop on f4, which is not a great square for the bishop in this structure since it cannot retreat to g3 should the need arise.

Black had the edge out of the opening not because black played some secret combination of moves, but simply because white did not make the best use of his pieces. So no, this is not a refutation.